CPT theorem

(particle physics) A theorem which states that a Lorentz invariant field theory is invariant to the product of charge conjugation C, space inversion P, and time reversal T.

A fundamental ingredient in quantum field theories, which dictates that all interactions in nature, all the force laws, are unchanged (invariant) on being subjected to the combined operations of particle-antiparticle interchange (socalled charge conjugation, C), reflection of the coordinate system through the origin (parity, P), and reversal of time, T. In other words, the CPT operator commutes with the hamiltonian. The operations may be performed in any order; TCP, TPC, and so forth, are entirely equivalent. If an interaction is not invariant under any one of the operations, its effect must be compensated by the other two, either singly or combined, in order to satisfy the requirements of the theorem. See also Quantum field theory.

The CPT theorem appears implicitly in work by J. Schwinger in 1951 to prove the connection between spin and statistics. Subsequently, G. Lüders and W. Pauli derived more explicit proofs, and it is sometimes known as the Lüders-Pauli theorem. The proof is based on little more than the validity of special relativity and local interactions of the fields. The theorem is intrinsic in the structure of all the successful field theories. See also Quantum statistics; Relativity; Spin (quantum mechanics).

CPT assumed paramount importance in 1957, with the discovery that the weak interactions were not invariant under the parity operation. Almost immediately afterward, it was found that the failure of P was attended by a compensating failure of C invariance. Initially, it appeared that CP invariance was preserved and, with the application of the CPT theorem, invariance under time reversal. Then, in 1964 an unmistakable violation of CP was discovered in the system of neutral K mesons. See also Parity (quantum mechanics).

One question immediately posed by the failure of parity and charge conjugation invariance is why, as one example, the π⁺ and π⁻ mesons, which decay through the weak interactions, have the same lifetime and the same mass. It turns out that the equality of particle-antiparticle masses and lifetimes is a consequence of CPT invariance and not C invariance alone. See also Elementary particle; Meson; Symmetry laws (physics).